Boundary Conditions Research Articles

Uncertainty Quantification Framework for High-Temperature Gas-Cooled Reactors Using VSOP and DAKOTA

Advanced nuclear reactors hold strong potential for clean and safe energy production. From the various designs, high-temperature gas-cooled reactors (HTGRs) are among the most promising ones. One fundamental aspect for their safety evaluation is the uncertainty quantification (UQ) of HTGR models. This study introduces a UQ framework developed around the VSOP code system. The framework uses the DAKOTA statistical toolkit to sample various case-dependent inputs, such as manufacturing parameters and boundary conditions. A Python driver script is developed to create an interface between DAKOTA and VSOP. Dedicated sampling modules are developed for perturbing the case-independent inputs that include: background microscopic cross sections, fission yields, decay constants, and resonance integral parameters. The capabilities of the UQ framework are demonstrated on an 80-MW(thermal) pebble-bed small modular reactor equilibrium core model. Four different UQ studies are performed to understand and quantify the impact of various sets of inputs. Initially, perturbations in the cross sections are analyzed, given their inherent complex nature. The results show that the predicted k eff uncertainty is ~420 pcm, a value consistent with those reported in the literature for pebble-bed reactors. The most statistically significant cross sections are the 235U number of average neutrons per fission, the 235U and 239Pu fission, and the 235U and 239Pu capture in thermal energies. Small uncertainties are obtained for the maximum burnup and fuel temperature, with values less than 0.15%. The second study assessed the additional impact of the fission yields and decay constants. The results show an impact of 50 pcm on the k eff , with a negligible impact on the other outputs of interest. The third study involved the perturbation of all the inputs, which resulted in unrealistically large uncertainties to most outputs due to the fuel kernel radius. This is attributed to the VSOP limitations for such uncertainty studies, since individual fuel kernels cannot be explicitly modeled, requiring the same fuel kernel radius perturbation to be applied in every coated particle for all fuel pebbles of the core. A more realistic approach is discussed and investigated in the fourth study. The results show that the cross sections remain the most important contributors for the k eff , the thermal flux distribution, and the power density distribution. However, for the maximum burnup, the maximum fuel temperature, and the gas temperature distribution, the power and mass flow rate boundary conditions are the most statistically significant inputs. Future work will aim to further refine and expand the VSOP UQ framework, and to perform code-to-code uncertainty comparison studies for different HTGR cores, such as the PBMR-400.

Deciphering the unique inertial focusing behavior of sperm cells.

Inertial focusing has been utilized to advance assisted reproductive technologies (ART) for animal breeding and in vitro fertilization (IVF) by separating sperm cells from biofluids with complex cell backgrounds. While existing studies have aimed to design and optimize sperm separation devices, the fundamental mechanism behind the unique focusing behavior of sperm in spiral channels remains largely unknown: sperm cells focus near the outer wall, whereas most other cells focus near the inner wall. This is primarily due to the lack of a direct modelling scheme for capturing the detailed inertial migration of sperm cells in the spiral channels. In this work, we developed a 3D DNS-PT modeling approach that can predict the inertial focusing of sperm cells with long tails. Unlike previous studies that considered rotating spheres, the novelty of our approach is in extracting the inertial lift force for a triaxial ellipsoid (which represents the asymmetric oval-shaped sperm head) and accounting for the tail effect through appropriate boundary conditions, thus capturing their cumulative impact on sperm focusing behavior. Furthermore, we conducted inertial microfluidics experiments with fluorescent images of spermatozoa to validate the modelling results. We discovered that the effect of the tail, rather than the sperm head shape or orientation, is the primary determinant of the unique inertial focusing position of sperm cells in microchannels. The modelling results provided significant insights into the evolution of particle distribution in the channel cross-section along the flow direction, which was previously unknown due to the limitations of imaging techniques. The predicted particle trajectories enabled detailed analysis and explanation of the distinct migration paths of sperm cells and spherical particles. This work bridges the gap in our understanding of the inertial migration of sperm and other flagellated cells, facilitating the better design and optimization of sorting and separation devices.

Generalized finite differences in the frequency domain method applied to finite photonic crystal

We propose a Generalized Finite-Difference in the Frequency-Domain method for the computation of photonic band-like structures of optical systems based on finite photonic crystals. Our approach is to discretize some spatial domain composed of multiple complete non-overlapping unit cells, such that boundary conditions of interest can be introduced into the eigenvalue problem, and then force Bloch wave conditions by means of a semi-unitary transformation, which also reduces the degrees of freedom. The validity and effectiveness of the proposed method are shown for the case of a one-dimensional photonic crystal embedded in an optical cavity. The limit from finite-to-infinite photonic crystals is reviewed in view of the proposed method.

A frequency-domain approach to molecular photoionization via driven Schrödinger equation.

This work extends the formalism introduced in a previous publication [T. Marx and S. I. Bokarev, Phys. Rev. A 106, 032806 (2022)] and provides a comprehensive framework for predicting molecular photoelectron spectra. This method employs a frequency-domain approach, formulated as a driven inhomogeneous Schrödinger equation under first-order perturbation theory with outgoing boundary conditions. It is shown to be analytically equivalent to Fermi's golden rule approach while offering a distinct physical interpretation tied directly to the measured photocurrent. The formalism incorporates detailed light-matter interactions, yielding unique solutions. The implementation strategy is discussed in depth, emphasizing computational efficiency and flexibility. The results are validated through comparisons with experimental data and other theoretical methods for atomic and small molecular systems and analytically solvable models.

Two direct sampling methods for an anisotropic scatterer with a conductive boundary

In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary condition. We will assume that the corresponding far–field pattern or Cauchy data is either known or measured. The conductive boundary condition models a thin coating around the boundary of the scatterer. We will develop two direct sampling methods to solve the inverse shape problem by numerically recovering the scatterer. To this end, we study direct sampling methods by deriving that the corresponding imaging functionals decay as the sampling point moves away from the scatterer. These methods have been applied to other inverse shape problems, but this is the first time they will be applied to an anisotropic scatterer with a conductive boundary condition. These methods allow one to recover the scatterer by considering an inner–product of the far–field data or the Cauchy data. Here, we will assume that the Cauchy data is known on the boundary of a region Ω that completely encloses the scatterer D. We present numerical reconstructions in two dimensions to validate our theoretical results for both circular and non-circular scatterers.

Transition between rotation- and buoyancy-dominated regimes in rotating convection: the effect of boundary conditions

In rotating convection, analysis of heat transfer reveals a distinct shift in behaviour as the system transitions from a steep scaling regime near the onset of convection to a shallower scaling at higher Rayleigh numbers ( $Ra$ ), irrespective of whether the top and bottom plates have stress-free, no-slip or no boundaries (homogeneous convection). However, while most research on this transition focuses on no-slip boundary conditions, geophysical and astrophysical flows commonly involve stress-free and homogeneous convection models as well. This study delves into the transition from the rapidly rotating regime to the non-rotating one with both stress-free and homogeneous models, leveraging direct numerical simulations (DNS) and existing literature data. Our findings unveil that for stress-free boundary conditions, the transitional Rayleigh number ( $Ra_T$ ) exhibits a relationship $Ra_T\sim Ek^{-12/7}$ , whereas for homogeneous rotating convection, $Ra_T\sim Ek^{-2}\, Pr$ , where $Ek$ denotes the Ekman number, and $Pr$ denotes the Prandtl number. Both of these relationships align with the data obtained through DNS.

Do you have the correct brand logo? Role of logo direction, perceived logo movement imagery and brand positioning

Purpose Previous research has mainly examined the effects of static versus kinematic brand logos on consumer responses. This paper aims to analyze the impact of dynamic brand logos on consumer behavior. Design/methodology/approach Hypotheses were tested through five experimental studies involving 1,914 participants recruited in China. Participants answered questions investigating the interactive effects of perceived logo movement imagery (dynamic vs static) and logo direction (toward the left vs right) under different brand positioning conditions (traditional vs modern). Findings This study finds that, for modern brand positioning, static brand logos toward the right (vs left) generate higher purchase intention, which is consistent with prior literature. This impact does not hold for dynamic logos. For traditional brand positioning, the opposite pattern is observed. Specifically, brand logos toward the left receive more favorable evaluations than those toward the right for static logos; whereas for dynamic logos, the effect disappears. Brand engagement mediates the interaction effect between logo direction and perceived logo movement imagery on brand attitude. Originality/value Despite most previous research focused on static or kinematic logos, only a few studies have investigated how dynamic logos influence consumer attitude, particularly regarding the impact of logo direction in dynamic contexts and boundary conditions. This study advances the literature by examining how logo direction and perceived movement imagery jointly affect consumers’ brand perceptions while also highlighting the moderating role of brand positioning and the underlying mechanism of brand engagement.

Hydraulic Response to Sea Level Rise in a Coastal Aquifer Extending under the Sea with a Cut-off Wall.

Seawater intrusion can cause the freshwater-saltwater interface to move inland toward coastal freshwater aquifers. Sea level rise has become a significant driver of this phenomenon. Installing cut-off walls along coastal aquifers is an effective engineering measure to mitigate seawater intrusion. However, most analyses of groundwater flow under sea level rise, particularly with cut-off walls, primarily rely on numerical methods, with limited analytical approaches available. In this study, we developed mathematical models for groundwater flow induced by sea level rise, dividing the coastal aquifer into offshore and inland regions along the cut-off wall. An unknown flow function was introduced as a boundary condition at the shared boundary. Using homogenization and the finite Fourier transform method, we derived analytical solutions for the two regions separately. A global coupling solution, achieving hydraulic continuity between the two regions, was obtained by applying the collocation method at the shared boundary. The validity of the solution was confirmed through comparisons with finite difference numerical simulations. Furthermore, we analyzed the impacts of factors such as sea level rise amplitude and cut-off wall embedment depth on hydraulic changes. The results indicate that increases in the amplitude of sea level rise significantly amplify hydraulic head changes in the inland aquifers, while deeper embedment of the cut-off wall enhances its effectiveness in preventing seawater intrusion. However, the model does not consider density differences between freshwater and saltwater or the dynamics of the saltwater-freshwater interface.

Role of soluble surfactant in linear stability of a liquid film flowing down a compliant substrate

A linear stability analysis of a soluble surfactant-laden liquid film flowing down a compliant substrate is performed. Our purpose is to expand the prior studies (Carpenter and Garrad 1985 J. Fluid Mech.155, 465–510; Alexander et al., 2020 J. Fluid Mech.900, A40) by incorporating a soluble surfactant into the flow configuration. As a result, we formulate the Orr–Sommerfeld-type boundary value problem and solve it analytically by using the long-wave series expansion as well as numerically by using the Chebyshev spectral collocation method in an arbitrary wavenumber regime for infinitesimal disturbances. The long-wave result reveals that surface instability is stabilized in the presence of a surfactant, whereas it is destabilized in the presence of a compliant substrate. These opposing impacts suggest an analytical relationship between parameters associated with the soluble surfactant and compliant wall, ensuring the same critical Reynolds number for the emergence of surface instability corresponding to both surfactant-laden film flow over a compliant wall and surfactant-free film flow over a non-compliant wall. In the arbitrary wavenumber regime, along with the surface mode, we identify two additional modes based on their distinct phase speeds. Specifically, the wall mode emerges in the finite wavenumber regime, while the shear mode emerges only when the Reynolds number is large. As the surfactant Marangoni number increases, the wall mode destabilizes, resulting in a different outcome from the surface mode. Moreover, increasing the value of the ratio of adsorption and desorption rate constants stabilizes surface instability but destabilizes wall mode instability. As a result, we perceive that the soluble surfactant-laden film flow is linearly more unstable than the insoluble one due to surface instability but linearly more stable than the insoluble one due to wall mode instability. Additionally, we see a peculiar behaviour of base surface surfactant concentration on the primary instability. In fact, it has a specific value depending on adsorption and desorption rate constants below which surface instability stabilizes but wall mode instability destabilizes, whereas above which an opposite phenomenon occurs. Finally, in the high-Reynolds-number regime, we can suppress shear mode instability by raising the surfactant Marangoni number and the ratio of adsorption and desorption rate constants when the angle of inclination is sufficiently small. Unlike surface instability, the base surface surfactant concentration exhibits both stabilizing and destabilizing influences on shear mode instability.

Local elliptic regularity for solutions to stationary Fokker–Planck equations via Dirichlet forms and resolvents

In this paper, we show that, for a solution to the stationary Fokker–Planck equation with general coefficients, defined as a measure with an L2-density, this density not only exhibits H1,2-regularity but also Hölder continuity. To achieve this, we first construct a reference measure μ=ρdx by utilizing existence and elliptic regularity results, ensuring that the given divergence-type operator corresponds to a sectorial Dirichlet form. By employing elliptic regularity results for homogeneous boundary value problems in both divergence and non-divergence type equations, we demonstrate that the image of the resolvent operator associated with the sectorial Dirichlet form has H2,2-regularity. Furthermore, through calculations based on the Dirichlet form and the H2,2-regularity of the resolvent operator, we prove that the density of the solution measure for the stationary Fokker–Planck equation is, indeed, the weak limit of H1,2-functions defined via the resolvent operator. Our results highlight the central role of Dirichlet form theory and resolvent approximations in establishing the regularity of solutions to stationary Fokker–Planck equations with general coefficients.

NUMERICAL ANALYSIS OF ENERGY TRANSFER ON MAGNETOHYDRODYNAMIC SILVER NANOFLUID FLOW IN CYLINDRICAL COORDINATE

The impact of energy transfer in the area of Engineering and chemical processing has consistently been a major factor affecting the efficiency of material parameters. By examining the numerical analysis of energy transfer on Magnetohydrodynamic silver nanofluid flow on the material parameters, one can proffer a solution on how it can be improved. Cylindrical coordinate was used with the combined models of thermal conductivity and effective viscosity. Following the transformation of the governing equations into ordinary differential equations, the equations were then non-dimensionalized. Utilising the Laplace Transform Technique for the Nusselt number, Sherwood number, and Skin friction with adjusted boundary conditions, we were able to derive four distinct equations. These equations are the continuity equation, the momentum equation, the energy equation, and the concentration equation. The solution obtained was subjected to numerical analysis which showcased the heterogeneous effects of the material parameters on the different profiles of the nanofluid while considering the Rosseland approximation ( ) for the effect of radiation term, the upshot in Prandtl number results in to decrease in the temperature profile of the nanofluid which confirmed energy transfer on MHD silver nanofluid flow. The Schmidt number, chemical potential, and radiation parameter brought about axiomatical energy transfer on MHD silver nanofluid flow with the nanoparticle volume fraction were also considered.

Stability analysis of a class of Langevin equations in the frame of generalized Caputo fractional operator with nonlocal boundary conditions

The main objective of the present paper is to establish the existence and uniqueness of solutions for the fractional Langevin equation involving the ϕ-Caputo fractional operator with nonlocal boundary conditions. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional Langevin differential equation, including the ϕ-Caputo fractional operator. Furthermore, some novel boundaries are selected to be considered as a problem. The existence of the solution is obtained by applying a fixed point theorem, and the uniqueness of the solution is obtained by using the Banach contraction mapping principle to the considered problem. Moreover, we discuss the Hyres-Ulam stability result. The manuscript is concluded with an illustrative example to corroborate the reported results. This study extends and generalizes various results in the literature and provides new insights into the qualitative behavior of fractional differential systems.

Exploring the nature of unethical pro-organisational behaviour in the hotel industry

ABSTRACT Nowadays, unethical behavior has increasingly attracted attention as one of the main challenges faced in the hospitality industry. However, it is still unclear why and when hospitality employees exhibit unethical pro-organizational behavior. Based on this gap, this study aims to hypothesize and test a research model revealing that organizational identification affects unethical pro-organizational behaviour through organizational collective narcissism and that moral disengagement moderates the effect of organizational collective narcissism on unethical pro-organizational behaviour. The data were gathered from five-star hotel employees and their managers. The results have uncovered that the direct impact of organizational identification on unethical pro-organizational behaviour is insignificant; however, the indirect impact of organizational identification on unethical pro-organizational behaviour via organizational collective narcissism is significant. In addition, the results have found that moral disengagement moderates the effect of organizational collective narcissism on unethical pro-organizational behaviour. This study makes several unique contributions to the literature. First, this study introduces organizational collective narcissism as a special form of collective narcissism to organizational studies to shed light on the relationship mechanism in question. Second, this study sheds light on the relationship between organizational collective narcissism and unethical pro-organizational behavior by revealing that moral disengagement is a critical boundary condition.

Drivers and constraints in an emerging rural biogas system: actors’ perceptions from Northern Savonia

BackgroundThe biogas niche is usually approached from a top-down perspective, and its actors are considered a unanimous advocacy group in the national policy discourse. This setting downplays the diversity of actors and their opinions at a subnational level. In this study, ten biogas actors from the farm-level, industry, regional administration, and potential end-users in the Finnish region of Northern Savonia were interviewed. The actors’ perceptions of the national and regional biogas sectors were explored.ResultsThe national biogas policy framework appears discontinuous, and statements regarding biogas targets are perceived as ambiguous, thus lacking creditability at a local level. The economic feasibility of rural biogas production places a strong boundary condition for the local biogas system. When moving from the national to a local level, individual actor’s perception of the optimal value chain becomes highlighted. Extending the actor network beyond the regional context was deemed vital for the long-term stability of the locally emergent biogas ecosystem. As municipalities can influence both production and consumption domains, they were called to play a more active role in constructing local biogas systems.ConclusionsThe results of this study provided three insights: (1) social, political, and environmental drivers influence the biogas sector in addition to techno-economic drivers; (2) drivers and constraints are perceived differently by actors in agricultural biogas production than by actors in distribution and end-use; and (3) the local biogas niche contains partly divergent perceptions of how the biogas system should be organised. Connecting actors early through joint planning and formulating case-by-case business models may help mediate any conflicts of interest.

Superradiance of Friedberg-Lee-Sirlin solitons

It has recently been pointed out that rotation in internal space can induce superradiance. We explore this effect in non-topological solitons of the two-field Friedberg-Lee-Sirlin model. This renormalizable model admits very large solitons, making the perturbative scattering equations highly sensitive to boundary conditions and requiring a relaxation method for their solution. We find that the energy extraction rate is strongly influenced by the mass hierarchy of the two scalars, and solitons with lower internal frequencies lead to more peaks in the spectra of the amplification factors. Additionally, we derive absolute bounds on the amplification factors for general ingoing modes using a linear fractional optimization algorithm and establish analytical bounds near the mass gap. Published by the American Physical Society 2025

Novel curcumin@HKUST-1 composite with enhanced visible light harvesting capacities for photocatalytic applications.

The HKUST-1 and related MOFs have been proposed as photocatalysts, nevertheless they presented certain limitations, e.g. poor visible light absorption. Thus, we propose the encapsulation of the photosensitizer curcumin (Cur) in HKUST-1 as a strategy to improve light absorption in the resultant Cur@HKUST-1 composite. The Cur@HKUST-1 was characterized by XRD, FTIR, TGA, UV-Vis, BET, SEM, and electrochemical experiments confirming the Cur infiltration in 2.5%, preserving crystalline structure of HKUST-1. DFT calculations for Cur@HKUST-1 in periodic boundary conditions were employed to elucidate the chemical structure, corroborating experimental evidence. Chronoamperometry experiments in dark and visible light irradiation showed 48% photocurrent density enhancement for Cur@HKUST-1vs.HKUST-1, corroborating the sensitization effect derived from Cur inclusion. As a result, Cur@HKUST-1, presented 1.2 times (20% higher) photocatalytic hydrogen evolution than free HKUST-1 under visible light irradiation, just by 2.5% Cur loading into the HKUST-1, demonstrating infiltration as a suitable, nonlinear, strategy to produce active MOFs for photocatalytic purposes.

Borderline behavior and propagating terrace for a free boundary problem with positive bistable nonlinearity under Dirichlet boundary conditions

Borderline behavior and propagating terrace for a free boundary problem with positive bistable nonlinearity under Dirichlet boundary conditions

On Spreading Resistance for an Isothermal Source on a Compound Flux Channel

Abstract Recently, Jain [ASME J. Heat Transfer, 220 (2024)] provided spreading-resistance formulas for an isothermal source on compound, orthotropic, semi-infinite, two-dimensional (axisymmetric) flux channels (tubes). The boundary condition (BC) in the source plane was a discontinuous convection (Robin) one. Along the source, a sufficiently-large heat transfer coefficient was imposed to approximate an isothermal condition; elsewhere, it was set to zero, imposing an adiabatic BC. An eigenfunction expansion resolved the problem. Distinctly, we impose, precisely, a mixed isothermal-adiabatic BC in the source plane and use conformal maps to resolve the spreading resistance for the limiting case of a compound, isotropic flux channel. Our approach requires more time to compute the spreading resistance. However, it converges uniformly rather than pointwise, converges to the exact spreading resistance rather than one with an error, eliminates the Gibbs phenomenon at the edges of the source and fully resolves the square-root singularities in heat flux as the discontinuity in the BC is approached.

Well‐Posedness Analysis and Numerics of Boundary‐Domain Integral Equation Systems Equivalent to the Robin Problem for the Helmholtz Equation With Variable Coefficients in Lipschitz Domains

ABSTRACTGiven the interior Robin boundary value problem (BVP) for the Helmholtz equation with variable coefficients, we use an appropriate parametrix to derive two boundary‐domain integral equation systems (BDIES) equivalent to the original Robin BVP in Lipschitz domains. One then can choose which BDIES might be more convenient to be solved numerically. Main results of the paper concern the equivalence between the BDIE systems obtained and the original BVP, as well as well‐posedness of the BDIES, which does not contain hypersingular operators. The last sections of the paper are devoted to confirm the theoretical results with various numerical experiments in 2D.

Nonlinear Guyer–Krumhansl equation and its boundary conditions in nanolayers

This paper deals with nonlinear effects in the Guyer–Krumhansl equation for nonlocal heat transport, both from the perspective of the boundary conditions (phonon–wall collisions) and of the bulk equation (phonon–phonon collisions) and explores their consequences on the effective thermal conductivity of nanosystems between two parallel layers or in two-dimensional ribbons. The nonlinearity arises from a dependence of the respective mean free paths on the values of the heat flux. The boundary conditions refer to slip heat flow along the limiting walls of the system, analogous to velocity slip flow along the walls in rarefied fluid dynamics. The effective thermal conductivity turns out to depend on the Knudsen numbers related to both mean free paths and on the temperature gradient.